RD Sharma Class 11 Solutions Chapter 23 Exercise 23.14 (Updated for 2021-22)

RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.14: Before taking the board exam, students can practise solving questions chapter-by-chapter and exercise-by-exercise to boost their confidence. RD Sharma Class 11 Maths Solutions Chapter 23 Exercise 23.14, pdf links are provided here to help students for this chapter.

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RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.14

This exercise provides an overview of the notion based on the relative positions of two points on a line. Students who are experiencing difficulty in comprehending concepts can use RD Sharma Class 11 Solutions. The solutions were developed by Kopykitab’s experts based on the students’ grasping ability.

Access answers to RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.14- Important Question with Answers

1. Find the values of α so that the point P(α ², α) lies inside or on the triangle formed by the lines x – 5y + 6 = 0, x – 3y + 2 = 0 and x – 2y – 3 = 0.

Solution:

Given: 

x – 5y + 6 = 0, x – 3y + 2 = 0 and x – 2y – 3 = 0 forming a triangle and point P(α², α) lies inside or on the triangle

Let ABC be the triangle of sides AB, BC and CA whose equations are x − 5y + 6 = 0, x − 3y + 2 = 0 and x − 2y − 3 = 0, respectively.

On solving the equations, we get A (9, 3), B (4, 2), and C (13, 5) as the coordinates of the vertices.

It is given that point P (α², α) lies either inside or on the triangle. The three conditions are given below.

(i) A and P must lie on the same side of BC.

(ii) B and P must lie on the same side of AC.

(iii) C and P must lie on the same side of AB.

If A and P lie on the same side of BC, then

(9 – 9 + 2)(α² – 3α + 2) ≥0

(α – 2)(α – 1) ≥ 0

α ∈ (- ∞, 1 ] ∪ [ 2, ∞) … (1)

If B and P lie on the same side of AC, then

(4 – 4 – 3) (α² – 2α – 3) ≥ 0

(α – 3)(α + 1) ≤ 0

α ∈ [- 1, 3] … (2)

If C and P lie on the same side of AB, then

(13 – 25 + 6)(α² – 5α + 6) ≥0

(α – 3)(α – 2) ≤ 0

α ∈ [ 2, 3] … (3)

From equations (1), (2), and (3), we get

α∈ [2, 3]

∴ α∈ [2, 3]

2. Find the values of the parameter a so that the point (a, 2) is an interior point of the triangle formed by the lines x + y – 4 = 0, 3x – 7y – 8 = 0, and 4x – y – 31 = 0.

Solutions:

3. Determine whether the point (-3, 2) lies inside or outside the triangle whose sides are given by the equations x + y – 4 = 0, 3x – 7y + 8 = 0, 4x – y – 31 = 0.

Solution:

We have provided complete details of RD Sharma Solutions Class 11 Maths Chapter 23 Exercise 23.14. If you have any queries related to CBSE Class 11, feel free to ask us in the comment section below.

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